Radial profiles for initial column density Σ and rotational velocity vrot for simulations with Rdisk = 100. The parameter gc indicates the resolution of the coarsest grid, lmax the deepest level of the resolution by dynamic refinement. The continous lines show simulations with Qinit = 1, the dashed lines simulations with Qinit = 3. The density distribution converges toward the analytic solution for higher refinement levels, i.e., the density gap in the inner part of the disk is smaller for higher refinement levels. Additionally, it is smaller for the simulation runs with Qinit = 1, which is due to the scale height dependency on the Q parameter (compare Eq. (23) and Fig. 3). The velocity, only nonzero within the disk matter, behaves analogous to the density.
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